2. What is the slope of a line that contains the points (4, 2) and (5,9)

The argument "All cats are mammals. I am a mammal. Therefore, I am a cat" is fallacious and can be shown as such using set theory and a Venn diagram.

Let's represent the sets using a Venn diagram:

   -------------

   |    Mammals   |

   -------------

       /       \

      /         \

     /           \

----          ----

| Cats |        | You |

----          ----

In the Venn diagram, the circle labeled "Mammals" represents the set of all mammals, and the circle labeled "Cats" represents the set of all cats. The region where the circles overlap represents the set of mammals that are also cats.

According to the argument, "All cats are mammals," which means that the set of cats is entirely contained within the set of mammals. This relationship is correctly represented in the Venn diagram.

The argument also states, "I am a mammal," which means that you are part of the set of mammals. In the Venn diagram, your position would be within the circle labeled "Mammals" but outside the circle labeled "Cats."

The fallacy occurs when the argument concludes, "Therefore, I am a cat." This conclusion is not valid because being a mammal does not automatically make you a cat. The Venn diagram clearly shows that there is a region within the set of mammals that is not within the set of cats.

To summarize, the fallacy in the argument arises from incorrectly inferring that being a mammal automatically implies being a cat. The Venn diagram visually demonstrates that being a mammal is a broader category that encompasses various animals, including cats, but being a mammal alone does not make one a cat.

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The equivalent expression to (2² x 3^4)^3 is given as follows:

2^6 x 3^12.

(first option).

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Hence the exponents for this problem are given as follows:

And the simplified expression is of:

2^6 x 3^12.

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Hi there! :)

\(\large\boxed{h(-4) + 2 = 4}\)

h(x) = 1/2x + 4

Substitute in -4 for "x" to solve for h(-4):

h(-4) = 1/2(-4) + 4

h(-4) = -2 + 4

h(-4) = 2

Since we are solving for h(-4) + 2, add:

2 + 2 = 4.

Answer:

4

Step-by-step explanation:

Step 1: Define

h(x) = 1/2x + 4

h(-4) = x = -4

Step 2: Substitute and Evaluate

h(-4) = 1/2(-4) + 4

h(-4) = -2 + 4

h(-4) = 2

Step 3: Find h(-4) + 2

2 + 2

4

Answer:

can you please show attachments?

You have to put a complete question in order for us to answer your question!

The equations of the lines that passes through the given points are:

Part A:

The slope of the line is given by:

m = (y2 - y1)/(x2 - x1) = (-2 - 3.5)/(10 - (-1)) = -0.5

Using the point-slope form of the equation of a line, where (x1, y1) = (-1, 3.5) and m = -0.5, we get:

y - 3.5 = -0.5(x + 1)

Simplifying, we get:

y = -0.5x + 2

Therefore, the equation of the line passing through the points (-1, 3.5) and (10, -2) is y = -0.5x + 2.

Part B:

The slope of the line is given by:

m = (y2 - y1)/(x2 - x1) = (9 - (-12))/(3 - (-4)) = 21/7 = 3

Using the point-slope form of the equation of a line, where (x1, y1) = (-4, -12) and m = 3, we get:

y - (-12) = 3(x - (-4))

Simplifying, we get:

y = 3x - 0

Therefore, the equation of the line passing through the points (-4, -12) and (3, 9) is y = 3x.

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Answer:

a.)In ∆BAC AND ∆DAC

ANGLE DAC = ANGLE BAC(GIVEN)

ANGLE DCA = ANGLE BCA (Given)

AD IS A COMMON SIDE

SO, ∆BAC congruence ∆DAC (A.S.A)

b.)Yes AB=AD (C.P.C.T.)

c.)Yes CD=CB(C.P.C.T.)

Hope that helps

No solution is the answer of inequality.

What is inequality

The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.  Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.

Given Data

\(\frac{4}{3}\)g - 3< g + \(\frac{2}{3}\) - \(\frac{1}{3}\)g

(\(\frac{4}{3}\)g - g) + \(\frac{1}{3}\)g <( \(\frac{2}{3}\) + 3)

Taking LCM,

\(\frac{4e+3e+1e}{3}\) < \(\frac{2+9}{3}\)

8g < 11

g < \(\frac{11}{8}\)

No solution is the answer of inequality.

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Answer:

38.28 .........................

Answer:

57.13..................................................

Step-by-step explanation:

Area of the square:

a^2: 4^2=16in^2

Area of the circle:

πr^2: π(4.5)^2= 63.6

Area of white part:

63.6 - 16 = 47.6

Probability of landing on square:

16/63.6 = 0.25

Probability of landing on white part:

63.6/16 = 3.975

Answer: b

Step-by-step explanation:

it is right

Sum of two smaller sides of a triangle must be greater than the largest side. So, the required range value is 7 < x < 23.

Important information:

Sum of two smaller sides of a triangle must be greater than the largest side.

If x is the largest side of the triangle, then

\(8+15>x\)

\(23>x\)         ...(i)

If 15 is the largest side of the triangle, then

\(x+8>15\)

\(x>15-8\)

\(x>7\)            ...(ii)

Using (i) and (ii), we get

\(7<x<23\)

Therefore, the required range value is \(7<x<23\).

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In 35mm single-lens camera the images produce negative that can be used as backups instead of using a digital camera.

A single-lens reflex camera (SLR) is a type of camera that typically employs a mirror and prism system (hence the word "reflex" from the reflection of the mirror) and allows the photographer to look through the lens to preview the exact scene that will be photographed.

Most SLR cameras have a mirror that swings out of the way of the light when the shutter button is depressed, allowing light to reach the light receptor and capturing the image.

The roof pentaprism found in the optical path between the reflex mirror and viewfinder of most SLR cameras enables upright and laterally accurate vision.

A camera's manual focus adjustment or an autofocus system's automated focus adjustment are both options.

The images produce negative that can be used as backups in 35mm single-lens camera instead of using a digital camera.

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9514 1404 393

Answer:

Step-by-step explanation:

1. The value can be read from the graph. At 3 units to the right of the vertical axis, the line is 3 units above the horizontal axis. The independent variable has a value of 3 at that point.

__

2. The dependent variable has a value of -5 at the next grid line just below the bottom of the graph shown. The value of the independent variable is -1 at that point.

Answer:

No Solution.

Step-by-step explanation:

y=-1-3x

y+3x=3

------------

-1-3x+3x=3

-1=3

no solution

Distance for the anchor drop every 5 seconds is,

⇒ E = 63 meters

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

A big ship drops its anchor.

Here, E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).

E = - 2.4t + 75

Now, Distance for the anchor drop every 5 seconds is,

Put t = 5;

E = - 2.4t + 75

E = - 2.4 × 5 + 75

E = - 12 + 75

E = 63 meters

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Answer:

The answer is A. f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0, because 2,000 of the bacteria remain alive.

Step-by-step explanation:

Answer:

The correct option is A.

Step by step explanation:

The exponential function is defined as

Where, a is initial value and b is growth factor or decay factor.

The initial population of bacteria is 5000.

After each day of treatment, 40% of the sample remains alive. It means the growth factor or decay factor is

Therefore the required function is

The horizontal asymptote is y=0 because

Therefore option A is correct.

Thus, the company must consider fixed monthly payments of amount $497.92 into the account to reach $97,000 in 13 years.

To find the monthly payment needed to reach $97,000 in 13 years, we can use the sinking fund formula:

FV = PMT * [(1 + i)^n - 1] / i

where:
FV = future value ($97,000)
PMT = monthly payment (unknown)
i = monthly interest rate (3.2% compounded monthly, which is 0.032 / 12 = 0.002667)
n = number of months (13 years * 12 months/year = 156 months)

Rearrange the formula to solve for PMT:

PMT = FV * i / [(1 + i)^n - 1]

PMT = 97,000 * 0.002667 / [(1 + 0.002667)^156 - 1]

PMT ≈ 497.92

So, the company should make fixed monthly payments of approximately $497.92 into the account to reach $97,000 in 13 years.

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The r-value ranges from -1 to +1, with -1 indicating a strong negative correlation. Therefore, the r-value closest to -1 represents the strongest negative correlation.

An r-value represents the strength and direction of a correlation between two variables. The strongest negative correlation occurs when the r-value is -1. In this case, as one variable increases, the other variable decreases consistently, showing a perfect negative linear relationship between the two variables.

The ability of a material to resist the flow of heat through it is gauged by the R-value , which is used in materials research and building construction. It measures the energy efficiency of insulation materials including fibreglass, foam board, and cellulose and is commonly represented in square metres kelvin per watt (m2K/W) units.

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The matrices [-3, 7; -2, 5] and [-5, 7; -2, 3] are multiplicative inverses since their product yields the identity matrix.

To determine whether two matrices are multiplicative inverses, we need to check if their product is the identity matrix.

Let's denote the given matrices as Matrix A and Matrix B:

Matrix A: [-3, 7; -2, 5]

Matrix B: [-5, 7; -2, 3]

To find the product of Matrix A and Matrix B, we perform matrix multiplication by multiplying the corresponding elements and summing the results:

[(-3)(-5) + 7(-2), (-3)(7) + 7(3)]

[(-2)(-5) + 5(-2), (-2)(7) + 5(3)]

Simplifying these calculations, we have:

[15 - 14, -21 + 21]

[10 - 10, -14 + 15]

Which results in:

[1, 0]

[0, 1]

The resulting matrix is the identity matrix, indicating that the product of Matrix A and Matrix B is indeed the identity matrix.

Therefore, we can conclude that Matrix A and Matrix B are multiplicative inverses of each other.

In summary, the matrices [-3, 7; -2, 5] and [-5, 7; -2, 3] are multiplicative inverses since their product yields the identity matrix.

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Answer:

3to the power of 2 times 5

Step-by-step explanation:

yeah thats all hehe

Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is expressed as y = mx+b

m is the slope

b is the intercept

Get the slope

m = -5-1/2-(-2)

m = -6/4

m = -3/2

Get the intercept

Substitute m = -3/2 and (-2, 1) into y = mx+c

1 = -3/2(-2) + c

1 = 3 + c

c = 1-3

c =-2

Get the required equation

y = mx+c

y = -3/2 x + (-2)

y  = -3/2 x -2

Hence the required equation is  y  = -3/2 x -2

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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The number of cookies in the jar initially was 42

To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.

We can use this information to set up the equation:

x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.

By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.

So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.

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The scale that Desmond used in the drawing is 11 inches : 4 feet

From the question, we have the following parameters that can be used in our computation:

Actual length of shopping center is 64 feet long

Scale length of shopping center is 176 inches long

using the above as a guide, we have the following:

Scale = Scale length : Actual length

substitute the known values in the above equation, so, we have the following representation

Scale = 176 inches : 64 feet

Simplify the ration

Scale = 11 inches : 4 feet

Hence, the scale that Desmond used in the drawing is 11 inches : 4 feet

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This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Answer:

9(x - 5)

Step-by-step explanation:

Just write the equation according to the sentence. It's THAT SIMPLE.

Answer:

d

Step-by-step explanation:

Answer:

62 minutes are required to cook 37 pounds of meat.

Step-by-step explanation:

Let cooking time = y

pounds of meat = x

So, The equation for this linear model will be:

y=(5/3)*x

Now, we need to find how long would be needed to cook 37 pounds of meat?

So x= 37

Putting it in linear model and finding value of x

y=(5/3)*37

y=62 minutes

So, 62 minutes are required to cook 37 pounds of meat.

Answer:

5

Step-by-step explanation:

-2 - (-7)

you have to do the opposite of the sign and switch the last number from neg to pos